Related papers: On electrostatic manifolds with boundary
In this article we continue our effort to do a systematic development of the solution theory for conformal formulations of the Einstein constraint equations on compact manifolds with boundary. By building in a natural way on our recent work…
Outer boundary conditions for strongly and symmetric hyperbolic formulations of 3D Einstein's field equations with a live gauge condition are discussed. The boundary conditions have the property that they ensure constraint propagation and…
On a finite-volume hyperbolic $3$-manifold, we establish an upper bound on the area of closed embedded surfaces with constant mean curvature at least one, depending on the mean curvature and the genus bounds. This area bound implies…
We investigate the properties of a fairly large class of boundary conditions for the linearised Einstein equations in the Riemannian setting, ones which generalise the linearised counterpart of boundary conditions proposed by Anderson.…
We provide a framework to build periodic boundary conditions on the pseudosphere (or hyperbolic plane), the infinite two-dimensional Riemannian space of constant negative curvature. Starting from the common case of periodic boundary…
We study Riemannian manifolds with boundary under a lower Ricci curvature bound, and a lower mean curvature bound for the boundary. We prove a volume comparison theorem of Bishop-Gromov type concerning the volumes of the metric…
A field theory on a three-dimensional manifold is introduced, whose field equations are the constraint equations for general relativity on a three-dimensional null hypersurface. The underlying boundary action consists of two copies of the…
In this paper we extend the classical BV framework to gauge theories on spacetime manifolds with boundary. In particular, we connect the BV construction in the bulk with the BFV construction on the boundary and we develop its extension to…
We study Riemannian manifolds $(M^n,g)$ with mean-convex boundary whose Ricci curvature is nonnegative in a spectral sense. Our first main result is a sharp spectral extension of a rigidity theorem by Kasue: we prove that under the…
We prove a formula relating the analytic torsion and Reidemeister torsion on manifolds with boundary in the general case when the metric is not necessarily a product near the boundary. The product case has been established by W. Lu\"ck and…
We establish the global $C^2$-estimates for the modified $\sigma_2$ curvature equation with prescribed boundary mean curvature, and particularly, the local boundary $C^2$ estimates on three-manifolds.
We prove that the 3-D compressible Euler equations with surface tension along the moving free-boundary are well-posed. Specifically, we consider isentropic dynamics and consider an equation of state, modeling a liquid, given by Courant and…
We study stationary free boundary configurations of an ideal incompressible magnetohydrodynamic fluid possessing nested flux surfaces. In 2D simply connected domains, we prove that if the magnetic field and velocity field are never…
Starting with a quantum particle on a closed manifold without boundary, we consider the process of generating boundaries by modding out by a group action with fixed points, and we study the emergent quantum dynamics on the quotient…
We study the simulation of charged systems in the presence of general boundary conditions in a local Monte Carlo algorithm based on a constrained electric field. We firstly show how to implement constant-potential, Dirichlet, boundary…
In this article, we study quasi-Einstein manifolds with constant scalar curvature. We provide a classification of compact and noncompact (possibly with boundary) $T$-flat quasi-Einstein manifolds with constant scalar curvature, where the…
We study the boundary and lens rigidity problems on domains without assuming the convexity of the boundary. We show that such rigidities hold when the domain is a simply connected compact Riemannian surface without conjugate points. For the…
An analogue of the Stefan-Sussmann Theorem on manifolds with boundary is proven for normal distributions. These distributions contain vectors transverse to the boundary along its entirety. Plain integral manifolds are not enough to…
This is a preliminary study of the equation of motion of Euclidean classical gravity on a graph, based on the Lin-Lu-Yau Ricci curvature on graphs. We observe that the constant edge weights configuration gives the unique solution on an…
If a variational problem comes with no boundary conditions prescribed beforehand, and yet these arise as a consequence of the variation process itself, we speak of a free boundary values variational problem. Such is, for instance, the…